Jordan Stoyanov, Probability measures and their moment (in)determinacy: Results and open questions
Datum objave: 25. 3. 2016
Seminar za algebro in funkcionalno analizo
Četrtek, 31. 3. 2016, ob 12:30 v predavalnici 2.04, FMF, Jadranska 21, Ljubljana
The discussion will be on and around the following fundamental fact:
Any probability measure with all moments finite is either uniquely characterized by its moment sequence (M-determinate) or it is non-unique (M-indeterminate). Well-known are classical results by
Stieltjes, Carleman, Cramer, Hausdorff, Krein, Berg, … In this talk
the emphasis will be on some very recent developments (Hardy’s
condition, rate of growth of the moments, Stieltjes classes). Further
progress can be made if we are able to answer a list of open questions
about the moment determinacy of probability measures in both dimension
1 and n. These are questions from real or complex Analysis (e.g.
dealing with systems of functional integral equations, Fourier
transform, factorization of measures, denseness of polynomials in some
spaces) and Algebra (e.g. dealing with infinite systems of algebraic
equations). A few statements will be reported to show that new ideas
and techniques are needed to challenge the open questions. Any
suggestion made during the talk or later will be more than welcome.